Please select a subject first
Advertisements
Advertisements
A carrom board (4 ft × 4 ft square) has the queen at the centre. The queen, hit by the striker moves to the from edge, rebounds and goes in the hole behind the striking line. Find the magnitude of displacement of the queen (a) from the centre to the front edge, (b) from the front edge to the hole and (c) from the centre to the hole.
Concept: undefined >> undefined
A mosquito net over a 7 ft × 4 ft bed is 3 ft high. The net has a hole at one corner of the bed through which a mosquito enters the net. It flies and sits at the diagonally opposite upper corner of the net. (a) Find the magnitude of the displacement of the mosquito. (b) Taking the hole as the origin, the length of the bed as the X-axis, it width as the Y axis, and vertically up as the Z-axis, write the components of the displacement vector.
Concept: undefined >> undefined
Advertisements
Suppose \[\vec{a}\] is a vector of magnitude 4.5 units due north. What is the vector (a) \[3 \vec{a}\], (b) \[- 4 \vec{a}\] ?
Concept: undefined >> undefined
Two vectors have magnitudes 2 m and 3m. The angle between them is 60°. Find (a) the scalar product of the two vectors, (b) the magnitude of their vector product.
Concept: undefined >> undefined
Let A1 A2 A3 A4 A5 A6 A1 be a regular hexagon. Write the x-components of the vectors represented by the six sides taken in order. Use the fact the resultant of these six vectors is zero, to prove that
cos 0 + cos π/3 + cos 2π/3 + cos 3π/3 + cos 4π/3 + cos 5π/3 = 0.
Use the known cosine values to verify the result.
Concept: undefined >> undefined
Let \[\vec{a} = 2 \vec{i} + 3 \vec{j} + 4 \vec{k} \text { and } \vec{b} = 3 \vec{i} + 4 \vec{j} + 5 \vec{k}\] Find the angle between them.
Concept: undefined >> undefined
Prove that \[\vec{A} . \left( \vec{A} \times \vec{B} \right) = 0\].
Concept: undefined >> undefined
If \[\vec{A} = 2 \vec{i} + 3 \vec{j} + 4 \vec{k} \text { and } \vec{B} = 4 \vec{i} + 3 \vec{j} + 2 \vec{k}\] find \[\vec{A} \times \vec{B}\].
Concept: undefined >> undefined
If \[\vec{A} , \vec{B} , \vec{C}\] are mutually perpendicular, show that \[\vec{C} \times \left( \vec{A} \times \vec{B} \right) = 0\] Is the converse true?
Concept: undefined >> undefined
Give an example for which \[\vec{A} \cdot \vec{B} = \vec{C} \cdot \vec{B} \text{ but } \vec{A} \neq \vec{C}\].
Concept: undefined >> undefined
A curve is represented by y = sin x. If x is changed from \[\frac{\pi}{3}\text{ to }\frac{\pi}{3} + \frac{\pi}{100}\] , find approximately the change in y.
Concept: undefined >> undefined
The electric current in a charging R−C circuit is given by i = i0 e−t/RC where i0, R and C are constant parameters of the circuit and t is time. Find the rate of change of current at (a) t = 0, (b) t = RC, (c) t = 10 RC.
Concept: undefined >> undefined
The changes in a function y and the independent variable x are related as
\[\frac{dy}{dx} = x^2\] . Find y as a function of x.
Concept: undefined >> undefined
Write the number of significant digits in (a) 1001, (b) 100.1, (c) 100.10, (d) 0.001001.
Concept: undefined >> undefined
Round the following numbers to 2 significant digits.
(a) 3472, (b) 84.16. (c)2.55 and (d) 28.5
Concept: undefined >> undefined
Is work-energy theorem valid in non-inertial frames?
Concept: undefined >> undefined
A ball is given a speed v on a rough horizontal surface. The ball travels through a distance l on the surface and stops. what are the initial and final kinetic energies of the ball?
Concept: undefined >> undefined
A ball is given a speed v on a rough horizontal surface. The ball travels through a distance l on the surface and stops. What is the work done by the kinetic friction?
Concept: undefined >> undefined
Consider the situation of the previous question from a frame moving with a speed v0 parallel to the initial velocity of the block. (a) What are the initial and final kinetic energies? (b) What is the work done by the kinetic friction?
Concept: undefined >> undefined
Can two particles be in equilibrium under the action of their mutual gravitational force? Can three particles be? Can one of the three particles be?
Concept: undefined >> undefined
